Data.Container.Base.Object.Instances

Definitions

Const2 : Type -> Type -> Cont

  Constant (non-dependent) container: positions do not depend on shapes
  As a polynomial functor: F(X) = aX^b

Visibility: public export

Const : Type -> Cont

  Constant container whose shapes and positions coincide
  As a polynomial functor: F(X) = aX^a

Visibility: public export

Nap : Type -> Cont

  Naperian container: a constant container with a single shape
  As a polynomial functor: F(X) = X^b

Visibility: public export

Flat : Type -> Cont

  Flat container: a constant container with a single position
  As a polynomial functor: F(X) = aX

Visibility: public export

Sharp : Type -> Cont

  Sharp container: a constant container without any positions
  As a polynomial functor: F(X) = a

Visibility: public export

Empty : Cont

  Empty container, isomorphic to Void
  As a polynomial functor: F(X) = 0
  Initial container

Visibility: public export

Scalar : Cont

  Container of a single thing
  As a polynomial functor: F(X) = X

Visibility: public export

UnitCont : Cont

  Container with a single shape, but no positions. Isomorphic to Unit : Type
  As a polynomial functor: F(X) = 1
  Terminal container

Visibility: public export

Pair : Cont

  Product, container of two things
  Isomorphic to Scalar >*< Scalar
  As a polynomial functor: F(X) = X^2

Visibility: public export

Either : Cont

  Coproduct, container of either one of two things
  Isomorphic to Scalar >+< Scalar
  As a polynomial functor: F(X) = X + X

Visibility: public export

Maybe : Cont

  Container of either one thing, or nothing
  Isomorphic to Scalar >+< UnitCont
  Initial algebra is Nat
  As a polynomial functor: F(X) = 1 + X

Visibility: public export

MaybeTwo : Cont

  Container of either two things, or nothing
  Isomorphic to Pair >+< UnitCont
  Initial algebra is BinTreeShape
  As a polynomial functor: F(X) = 1 + X^2

Visibility: public export

List : Cont

  List, container with an arbitrary number of things
  As a polynomial functor: F(X) = 1 + X + X^2 + X^3 + ...

Visibility: public export

Vect : List .Shp -> Cont

  Vect, container of a fixed/known number of things
  As a polynomial functor: F(X) = X^n

Visibility: public export

Grid : (List .Shp, List .Shp) -> Cont

  Grid, container of things arranged along two axes
  As a polynomial functor: F(X) = X^(hw)

Visibility: public export

Stream : Cont

  Container of an infinite number of things
  As a polynomial functor: F(X) = X^Nat

Visibility: public export

BinTree : Cont

  Container of things stored at nodes and leaves of a binary tree
  As a polynomial functor: F(X) = 1 + 2X + 3X^2 + 7X^3 + ...

Visibility: public export

BinTreeNode : Cont

  Container of things stored at nodes of a binary tree
  As a polynomial functor: F(X) = 1 + X + 2X^2 + 5X^3 +

Visibility: public export

BinTreeLeaf : Cont

  Container of things stored at leaves of a binary tree
  As a polynomial functor: F(X) = X + X^2 + 2X^3 + 5X^4 +

Visibility: public export

Tensor : List Cont -> Cont

  Tensors are containers
  As a polynomial functor: F(X) = ?

Visibility: public export

CartesianTensor : List Cont -> Cont

Visibility: public export

HancockTensor : List Cont -> Cont

Visibility: public export

CoproductTensor : List Cont -> Cont

Visibility: public export

ContUniverse : Cont

  Ignoring universe levels here
  This should be the analogue of `Type : Type`

Visibility: public export

Sample : Nat -> Cont

  Given a natural number `n`, this is a container whose shape represents a 
  distribution over `n` choices, and its position represents the choice made.

Visibility: public export